mtn bike?

fast bike?

Physics would suggest that the critical component is the power output, not the manner in which the power is generated. Physiologically, the effect will be different on the rider as the engine... So, if everything is equal except for the gearing used they should be equal. The benefit in a greater range of gears should be your ability to consistently produce the power output and leverage it between muscular and cardio systems...

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same power, different force.

please explain. I'm not sure if you agree with me or my buddy.

You're using "gear size" opposite from most people. A "big gear" usually means high gear inches, i.e. more torque and lower cadence for a given speed.

Anyway, you're basically right: if the rider is maintaining the same power output, a bike with less resistance will go faster, regardless of whether that power was produced at 40rpm or 90rpm.

Bottoming out your gearing can make you slower, because it reduces your power output. So a low-geared "slow" bike can sometimes beat a high-geared "fast" bike on a climb, if the rider produces enough extra power from the more-suitable gearing to make up for the increased resistance of the "slow" bike.

Power = torque x angular speed (cadence) = Force x crankarm length x cadence. To maintain the same power and a lower cadence, a higher force is required.

The power to get up the hill is independent of the gearing. The power required is a function of the opposing forces (gravity, aero drag, rolling resistance) and the speed. So to use less power and go faster, one of those forces needs to be reduced, not the gearing.

Gearing is a separate conversation because there is a practical limit to the force we can put out and we have preferred cadence ranges.

Right, oops, I realized that after I posted.


Wait, I'm confused by 2 things: 1) you're using "power" and "resistance" as if they mean different things, although to me "power" and "resistance" is the same thing. Please clarify. And, 2) you said "you're ... right", but it seems like you're saying that my buddy was right if you're saying that "less resistance will go faster". Please clarify.



this is the point at issue, but please clarify a little more. Like why are low-geared "slow" bikes more favorable on hilly climbs if I can just produce the same power on my high-geared "fast" bike? (I'm adopting your gearing vernacular here).

Oh, geez, I'm still confused. you're using "power" and "force" as if those are different, although they mean the same to me. Please distinguish what you mean by these two terms. Remember this is of the utmost importance because it's an argument with a buddy where I think I'm right. Very high importance factor.

You are right; your friend is wrong.

Your friend is mistaking pedal force for power. Power is the rate at which you are doing something (work). Power is essentially pedal force times cadence*. So, one bike will have lower pedal force times a higher RPM, while the other bike will have higher pedal force times lower RPM. Assuming that both bikes are moving up the hill at the same speed, they will have identical power. So, the higher/lower pedal forces and cadences are offsetting.

(* there is more to it than this, because crank length is important, but I left that out for the simplicity of the explanation.)

They are different. Power is a function of force.

Force = Mass x acceleration

Power = Force x velocity

OK, my apologies in advance for not understanding this (ironically, if I was indeed correct in my argument). But, when I look at my power meter at it tells me I'm riding up this hill at 300w, then is that what you're using for "force" or "power"? I'm assuming it's power, but I want to make sure.

Well, maybe, we're both making that mistake. I'm using "power" as the watts from my power meter. Like when I'm riding and my power meter tells me I'm going up this hill at 300w. Is that how you're using it?

Let me restate my issue in my terms (sorry, you gotta dumb it down for me). I think if I ride my bike up the hill at 300w in both bikes that I'll go forward up the hill at the same rate. My buddy thinks that one bike (the mtn bike) can go at 200w at a nice high cadence; whereas, the other bike (the tt bike) can go at 300w at a arduously low cadence. Both bikes in that situation are moving at the same rate. Thus, in my buddy's situation (if he's right), obviously that's why people choose the mtn bike as they whoof up hills at high cadence and low watts (my "power"). Am i right or my buddy?

Again, 300 watts is just that--300 watts. It doesn't matter what cadence or gearing combination you use to produce the 300 watts as long as it is steady. The difference will be in how difficult it is to maintain an even application of power. An easier gearing combination (say 39t-28t cog) will mean you're hitting a higher cadence and likely to maintain a steadier, more even application of power than you would running say a 53t-14t and standing.

Now, the other factors involved in getting up the hill faster are huge such as drivetrain losses, power loss due to suspension play, differing weights in bicycles, ability to smoothly pedal your chosen gearing combo, etc. But, if all things are equal except for your gear ratio, it's all the same.

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Yes, Watts is Power.

I'm using "resistance" to refer to the stuff slowing the bike down, like rolling resistance and gravity and aerodynamics. On the road, mountain bikes tend to deal with higher resistances than road bikes, so they go slower when pedaled at the same power.

When I said "resistance", you were thinking of pedal resistance, I assume?

Anyway, they're not the same thing. Imagine that you have a bike on a steep hill, and it's in a high gear, and you stand on the pedal but it doesn't move at all because your gearing is too high. In that case, you're putting lots of force on the pedal, and the pedal has lots of resistance, but your power output is 0.

Power is produced from force and motion. It's the rate of motion of the pedals multiplied by the force that you're pushing on them.

If you produce the same power on both bikes, then the low-geared "slow" bike would not be favorable.

 
If you use a bigger gear (low gear in your terminology), you'll go farther with each turn of the pedals, so you'll go a lot faster for the same effort.

(I'm kidding)

I have heard that argument from runners: "your legs are twice as long, so you go twice as far with each step, so you should go twice as fast" or "it takes half the effort for you as it does for me".

I counter that stride length is actually not very correlated to leg length and anyway it doesn't work that way. I then usually give the gear analogy. I'm an engineering professor and am kinda a d!ck when people don't understand mechanics.

Those of you who are saying if it's the same power, it's the same speed (if the same efficiency and weight) are right.

Power = work/time
Work = force x distance (in direction of force)

So the same weight going up the same hill with the same power will go the same speed whether its 1 rpm or 500 rpm. Your ability to deliver that power and your efficiency may be a function of cadence, but same power = same speed if all else is equal.

You can simplify this even more. Don't worry about two bikes, just consider your two ends of the gearing on a single bike.

If you find a long steady slope hill and ride along at a steady speed, you can shift to whatever gear you like and your power will not change. Your cadence will certainly change (faster feet with lower gears), but the power is constant.

As mentioned above, if you have to grind at 40RPM with a huge gear, it will feel a lot harder versus your favorite spinning speed, but the power is still the same.

All things being equal a road bike will be quicker up hill than a mountain bike, 1. mountain bikes are heavier and 2.have wider tyres that have more drag 3. have a more upright seating position that is less aero.
However If the length of the hill is long enough or steep enough and/or the rider is unfit, the mountain bike will be faster if the road bike rider is forced to walk or is not strong enough to pedal at such a low cadence.
Believe me if it was quicker up hill the riders in the grand tours would all swap bikes at the bottom of mountains. There is a move to lower gearing in the pro peloton though

Here's a little test I did a few years ago to illustrate this point for a co-worker. I rode in 3 different gear combinations and cadences: 50x11 @ 47rpm, 50x19 @ 80rpm, and 50x25 @ 109rpm. But my power and speed remained constant (16.5mph @ 143w)...

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"I'm thinking of a number between 1 and 10, and I don't know why!"

'Force' as a term of Physics has a more specific meaning than just the casual usage to describe "how hard I'm mashing the pedal down"... technically, it's mass x acceleration. **Algebra Alert** Acceleration is velocity over time. Velocity is distance over time (in other words, acceleration is distance over time ^2; hence velocity is an average value, whereas acceleration can account for a rate of change in velocity).

Maybe it's easier to think of another term, 'work' ~ how much energy it takes to move an object a certain distance. At least in the abstract, that amount of work is the same regardless of how long it takes, i.e., whether it's applied more gradually or more quickly (obviously in the real world, there are other confounding variables in the mix like gravity & wind drag). To move it more quickly takes more force (i.e., same work numerator over smaller time denominator = greater output value). Power is force over time, so like the relationship between velocity and acceleration, power accounts for the rate at which that force is delivered.

I'm actually starting to confuse myself now; it's been way too long since my last physics class. Someone else will undoubtedly correct me if i've gotten some of it jumbled. Essentially though, from a physics standpoint, the gearing is utterly irrelevant to the energy it takes to move 2 different bikes of equal mass (including the rider, of course) up the same grade at the same speed. It only matters in terms of the physiological efficiency translated to the effort level of the rider, which is more evident at either extreme (high vs low cadence) but within the 'normal' range has more to do w/ the individual rider's preference. Of course, there's also the physiological variable of standing vs sitting, and even mixing it up on a long climb to vary the muscle groups vs fatigue, etc. So gearing will certainly effect THAT, which in turn can color your perception of power on the road, but again as long as you're moving equal masses at the same speed, the actual power equation is unaffected by whether your legs are propelling it a high or low cadence.

This is the absolute perfect illustration.

Back to OP, as a basic physics definition, if it takes 300W to ride up a given hill at 10 MPH, it does not matter how fast or slow you pedal (gearing), it will always take 300W to ride up that hill at 10 MPH.

No back to the perfect illustration. How it feels while producing that power will be radically different. At 40 RPM, you will be absolutely mashing the pedals and relying heavily on anaerobic strength. At 100 RPM, your pedal force will be much lighter, and your heart will be higher (see illustration) because that is aerobic. Some people are wired more for low cadence anaerobic climbing while other are spinners who can substitute aerobic (heart rate) for less pedal force.